Optimal. Leaf size=43 \[ -\frac {12}{1375 (3+5 x)^2}+\frac {201}{15125 (3+5 x)}+\frac {20 \log (6-x)}{3993}+\frac {1493 \log (3+5 x)}{499125} \]
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Rubi [A]
time = 0.02, antiderivative size = 43, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {1607, 153}
\begin {gather*} \frac {201}{15125 (5 x+3)}-\frac {12}{1375 (5 x+3)^2}+\frac {20 \log (6-x)}{3993}+\frac {1493 \log (5 x+3)}{499125} \end {gather*}
Antiderivative was successfully verified.
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Rule 153
Rule 1607
Rubi steps
\begin {align*} \int \frac {-x^2+x^3}{(-6+x) (3+5 x)^3} \, dx &=\int \frac {(-1+x) x^2}{(-6+x) (3+5 x)^3} \, dx\\ &=\int \left (\frac {20}{3993 (-6+x)}+\frac {24}{275 (3+5 x)^3}-\frac {201}{3025 (3+5 x)^2}+\frac {1493}{99825 (3+5 x)}\right ) \, dx\\ &=-\frac {12}{1375 (3+5 x)^2}+\frac {201}{15125 (3+5 x)}+\frac {20 \log (6-x)}{3993}+\frac {1493 \log (3+5 x)}{499125}\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 33, normalized size = 0.77 \begin {gather*} \frac {\frac {99 (157+335 x)}{(3+5 x)^2}+2500 \log (-6+x)+1493 \log (3+5 x)}{499125} \end {gather*}
Antiderivative was successfully verified.
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Mathics [A]
time = 1.97, size = 43, normalized size = 1.00 \begin {gather*} \frac {15543+33165 x+\left (9+30 x+25 x^2\right ) \left (1493 \text {Log}\left [\frac {3}{5}+x\right ]+2500 \text {Log}\left [-6+x\right ]\right )}{4492125+14973750 x+12478125 x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 34, normalized size = 0.79
method | result | size |
risch | \(\frac {\frac {201 x}{3025}+\frac {471}{15125}}{\left (3+5 x \right )^{2}}+\frac {20 \ln \left (-6+x \right )}{3993}+\frac {1493 \ln \left (3+5 x \right )}{499125}\) | \(30\) |
norman | \(\frac {-\frac {113}{3025} x -\frac {157}{1815} x^{2}}{\left (3+5 x \right )^{2}}+\frac {20 \ln \left (-6+x \right )}{3993}+\frac {1493 \ln \left (3+5 x \right )}{499125}\) | \(33\) |
default | \(\frac {20 \ln \left (-6+x \right )}{3993}-\frac {12}{1375 \left (3+5 x \right )^{2}}+\frac {201}{15125 \left (3+5 x \right )}+\frac {1493 \ln \left (3+5 x \right )}{499125}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 34, normalized size = 0.79 \begin {gather*} \frac {3 \, {\left (335 \, x + 157\right )}}{15125 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} + \frac {1493}{499125} \, \log \left (5 \, x + 3\right ) + \frac {20}{3993} \, \log \left (x - 6\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.32, size = 53, normalized size = 1.23 \begin {gather*} \frac {1493 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 2500 \, {\left (25 \, x^{2} + 30 \, x + 9\right )} \log \left (x - 6\right ) + 33165 \, x + 15543}{499125 \, {\left (25 \, x^{2} + 30 \, x + 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.08, size = 32, normalized size = 0.74 \begin {gather*} \frac {1005 x + 471}{378125 x^{2} + 453750 x + 136125} + \frac {20 \log {\left (x - 6 \right )}}{3993} + \frac {1493 \log {\left (x + \frac {3}{5} \right )}}{499125} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.00, size = 41, normalized size = 0.95 \begin {gather*} \frac {20}{3993} \ln \left |x-6\right |+\frac {1493}{499125} \ln \left |5 x+3\right |+\frac {\frac {1}{66550} \left (4422 x+\frac {10362}{5}\right )}{\left (5 x+3\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.23, size = 29, normalized size = 0.67 \begin {gather*} \frac {20\,\ln \left (x-6\right )}{3993}+\frac {1493\,\ln \left (x+\frac {3}{5}\right )}{499125}+\frac {\frac {201\,x}{75625}+\frac {471}{378125}}{x^2+\frac {6\,x}{5}+\frac {9}{25}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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